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On the spectrum of Euler–Bernoulli beam equation with Kelvin–Voigt damping

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
374
Issue
1
Identifiers
DOI: 10.1016/j.jmaa.2010.08.070
Keywords
  • Beam Equation
  • Spectrum
  • Variable Coefficients
  • Kelvin–Voigt Damping
Disciplines
  • Mathematics

Abstract

Abstract The spectral property of an Euler–Bernoulli beam equation with clamped boundary conditions and internal Kelvin–Voigt damping is considered. The essential spectrum of the system operator is rigorously identified to be an interval on the left real axis. Under some assumptions on the coefficients, it is shown that the essential spectrum contains continuous spectrum only, and the point spectrum consists of isolated eigenvalues of finite algebraic multiplicity. The asymptotic behavior of eigenvalues is presented.

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